In reply to Frank the Husky:
Not sure about joining, but OeAV (so Austrian) or DAV (German) are options. Roughly the same price, but with insurance and so on added benefits.
The discount is always the same with any reciprocal card, but in in certain cases If the refuge is operated by a local branch/division of the CAI, they might get even better price. Not sure If this is How CAI operates, but certainly the case with OeAV (which is why I’m A member of Sektion Salzburg, not the UK branch).
As for the discount, it varies but I’m sure you’ll find the prices online somewhere. I recall Gianetti was ~40 Eur for halfboard instead or ~55 or so. So 3 to 4 nights and you’be saved the BMC card value.